De-Ramping
How De-Ramping Maps Range to Frequency
A linear frequency-modulated (LFM) waveform sweeps its instantaneous frequency linearly across a bandwidth B during a pulse of length T, giving a chirp rate of α = B/T hertz per second. When the echo from a target at range R arrives, it is a time-delayed copy of the transmitted chirp, shifted by the round-trip delay τ = 2R/c. De-ramping multiplies this echo by a local replica of the transmitted ramp (or a slightly offset reference). Since both ramps climb at the same slope, the difference frequency produced by the mixer is constant for the duration of the overlap: fb = ατ = (B/T)(2R/c). The receiver has converted distance into a pure tone.
This is enormously efficient. A radar that wants 15 cm range resolution needs B = 1 GHz, which would normally demand a 2 Gsps converter to satisfy Nyquist across the full pulse bandwidth. With de-ramping, only the spread of beat frequencies within the range swath must be digitized. A 150 m deep scene maps to roughly 10 MHz of beat bandwidth (2BN/cT), so a 25 to 30 Msps ADC is sufficient, a reduction of nearly two orders of magnitude in sampling rate, data volume, and power. The penalty is a residual video phase (RVP) term and a small range-dependent time skew that the processor must compensate before forming imagery.
The technique constrains the geometry it can observe. Because the beat frequency rises with range, the ADC's usable bandwidth defines how deep a range window can be unambiguously sampled, and the finite duration of the reference ramp means very distant returns stop overlapping the local replica and fall out of the dwell. Designers therefore pick the reference delay to center the swath of interest, and they pair de-ramping with stop-band filtering so that out-of-swath clutter does not alias into the band of valid beats.
Governing Equations
α = B / T (Hz/s)
Beat frequency vs. range:
fb = α × τ = (B / T) × (2R / c)
Range resolution (set by bandwidth):
ΔR = c / (2B)
Unambiguous range window (set by ADC):
Rwindow = (c × T × fADC) / (2B)
Where B = chirp bandwidth, T = pulse duration, τ = round-trip delay, R = target range, c ≈ 3×108 m/s, fADC = ADC bandwidth. Example: B = 1 GHz, T = 100 μs → α = 1013 Hz/s; a target at R = 75 m (τ = 0.5 μs) gives fb ≈ 5 MHz and ΔR = 15 cm.
De-Ramping vs. Direct Digital Pulse Compression
| Parameter | De-Ramping (Stretch) | Direct Matched Filter | Notes |
|---|---|---|---|
| ADC bandwidth needed | Beat span only (~1 to 50 MHz) | Full chirp B (up to GHz) | De-ramp wins for wideband |
| Dechirp location | Analog mixer, pre-ADC | Digital correlator, post-ADC | Hardware vs. software |
| Range resolution | c/(2B) ≈ 15 cm @ 1 GHz | c/(2B) ≈ 15 cm @ 1 GHz | Same, set by B |
| Range coverage | Limited swath window | Full unambiguous range | Stretch trades swath for rate |
| Range profile via | FFT of beat record | Correlation / FFT | Both end in frequency domain |
| Main artifacts | RVP, range-dependent skew | Range sidelobes | Both correctable in processing |
Frequently Asked Questions
How does de-ramping reduce the ADC sampling rate for a wideband chirp?
Mixing the echo against a reference replica of the ramp maps each target to a beat at fb = (B/T)(2R/c). A scene only N meters deep occupies just 2BN/(cT) of beat bandwidth. For a 1 GHz, 100 μs chirp over a 150 m window the beats span about 10 MHz, so a 25 to 30 Msps ADC replaces a 2 Gsps converter. That is the core advantage of stretch processing.
What sets the range resolution and unambiguous range window of a de-ramped system?
Resolution is ΔR = c/(2B), fixed by chirp bandwidth and independent of de-ramping; 1 GHz gives 15 cm. The range window is set by ADC bandwidth, Rwindow = c·T·fADC/(2B). Targets beyond that, or beyond the reference-ramp overlap, fold or drop out, so the reference delay is chosen to center the swath of interest.
How does de-ramping differ from matched-filter pulse compression?
A matched filter digitizes the full chirp bandwidth then correlates against a stored replica. De-ramping does the correlation in an analog mixer, so only the residual beat bandwidth is sampled and an FFT replaces the filter. The cost is residual video phase and a range-dependent time skew to correct, plus tighter swath limits, in exchange for far lower ADC cost and power.